#define _CRT_SECURE_NO_WARNINGS

class Solution {
public:
    int integerBreak(int n) {
        vector<int> dp(n + 1, 0);
        dp[0] = 0;
        dp[1] = 0;
        dp[2] = 1;
        for (int i = 3; i <= n; i++)
        {
            for (int j = 2; j < i; j++)
            {
                dp[i] = max(dp[i], max(dp[i - j] * j, (i - j) * j));
            }
        }
        return dp[dp.size() - 1];
    }
};

class Solution {
public:
    int integerBreak(int n) {
        vector<int> dp(n + 1, 0);
        dp[0] = 0;
        dp[1] = 0;
        dp[2] = 1;
        for (int i = 3; i <= n; i++)
        {
            for (int j = 1; j < (i / 2 + 1); j++)
            {
                dp[i] = max(dp[i], max(dp[i - j] * j, (i - j) * j));
            }
        }
        return dp[dp.size() - 1];
    }
};

class Solution {
public:
    int numTrees(int n) {
        vector<int> dp(n + 1, 0);
        dp[0] = 1;
        for (int i = 1; i <= n; i++)
        {
            for (int j = 1; j <= i; j++)
            {
                dp[i] += dp[j - 1] * dp[i - j];
            }
        }
        return dp[dp.size() - 1];
    }
};